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Kepler's 1st Law: Orbits are Elliptical

With Tycho Brahe's observations, Kepler set out to determine if the
paths of the planets could be described with a curve. By trial and
error, he discovered that an ellipse with the Sun at one focus could
accurately describe the orbit of a planet about the Sun.

Ellipses are described mainly by the length of their two axes. A
circle has the same diameter whether you measure it across or up and
down. But an ellipse has diameters of different lengths. The longest
one is called the major axis, and the shortest one is the minor axis.
The ratio of these two lengths determines the eccentricity
(e) of the ellipse; it's a measure of how elliptical it is.
Circles have e=0, and very stretched-out ellipses have an eccentricity
nearly equal to 1.

Planets do move on ellipses, but they are nearly circular. Comets are
a good example of objects in our solar system that may have very
elliptical orbits. Compare the eccentricities and orbits of the
objects in the diagram.

Once Kepler figured out that planets move around the Sun on
ellipses, he then discovered another interesting fact about
the speeds of planets as they go around
the Sun.

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